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Derivative of:
1/3x^3-3x^2+5x+10
Identical expressions
one / three x^3-3x^ two +5x+ ten
1 divide by 3x cubed minus 3x squared plus 5x plus 10
one divide by three x cubed minus 3x to the power of two plus 5x plus ten
1/3x3-3x2+5x+10
1/3x³-3x²+5x+10
1/3x to the power of 3-3x to the power of 2+5x+10
1 divide by 3x^3-3x^2+5x+10
1/3x^3-3x^2+5x+10dx
Similar expressions
1/3x^3+3x^2+5x+10
1/3x^3-3x^2+5x-10
1/3x^3-3x^2-5x+10

Solving integrals/ 1/3x^3-3x^2+5x+10

Integral of 1/3x^3-3x^2+5x+10 dx

The solution

You have entered [src]

  1                          
  /                          
 |                           
 |  / 3                  \   
 |  |x       2           |   
 |  |-- - 3*x  + 5*x + 10| dx
 |  \3                   /   
 |                           
/                            
0

$$\int\limits_{0}^{1} \left(\frac{x^{3}}{3} - 3 x^{2} + 5 x + 10\right)\, dx$$

Integral(x^3/3 - 3*x^2 + 5*x + 10, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{x^{3}}{3}\, dx = \frac{\int x^{3}\, dx}{3}$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{3}\, dx = \frac{x^{4}}{4}$
  So, the result is: $\frac{x^{4}}{12}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 3 x^{2}\right)\, dx = - \int 3 x^{2}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 3 x^{2}\, dx = 3 \int x^{2}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{2}\, dx = \frac{x^{3}}{3}$
    So, the result is: $x^{3}$
  So, the result is: $- x^{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 5 x\, dx = 5 \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $\frac{5 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 10\, dx = 10 x$
The result is: $\frac{x^{4}}{12} - x^{3} + \frac{5 x^{2}}{2} + 10 x$
Now simplify:

$\frac{x \left(x^{3} - 12 x^{2} + 30 x + 120\right)}{12}$
Add the constant of integration:

$\frac{x \left(x^{3} - 12 x^{2} + 30 x + 120\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{3} - 12 x^{2} + 30 x + 120\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                     
 |                                                      
 | / 3                  \                       4      2
 | |x       2           |           3          x    5*x 
 | |-- - 3*x  + 5*x + 10| dx = C - x  + 10*x + -- + ----
 | \3                   /                      12    2  
 |                                                      
/

$$\int \left(\frac{x^{3}}{3} - 3 x^{2} + 5 x + 10\right)\, dx = C + \frac{x^{4}}{12} - x^{3} + \frac{5 x^{2}}{2} + 10 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

139
---
 12

$$\frac{139}{12}$$

139
---
 12

$$\frac{139}{12}$$

Упростить

Numerical answer [src]

11.5833333333333

11.5833333333333

The graph

Use the examples entering the upper and lower limits of integration.

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Integral of 1/3x^3-3x^2+5x+10 dx

Limits of integration:

The graph:

Piecewise:

The solution